On the Hilbert scheme of linearly normal curves in Pr\mathbb{P}^r with small index of speciality

We study the Hilbert scheme of smooth, irreducible, non-degenerate and linearly normal curves of degree $d$ and genus $g$ in $\mathbb{P}^r$ whose complete and very ample hyperplane linear series $\mathcal{D}$ have relatively small index of speciality $i(\mathcal{D})=g-d+r$. In particular we show the existence and the non-existence of certain Hilbert schemes with $i(\mathcal{D})=4$. We also determine the irreducibility of $\mathcal{H}^\mathcal{L}_{2r+4,r+8,r}$ for $3\le r\le 8$, which are rather peculiar families in some sense.Comment: 25 pages. Comments are very welcome. arXiv admin note: text overlap with arXiv:2101.0055

On the Hilbert scheme of linearly normal curves in Pr\mathbb{P}^r with small index of speciality

We study the Hilbert scheme $\mathcal{H}^\mathcal{L}_{d,g,r}$ parametrizing smooth, irreducible, non-degenerate and linearly normal curves of degree $d$ and genus $g$ in $\mathbb{P}^r$ whose complete and very ample hyperplane linear series $\mathcal{D}$ have relatively small index of speciality $i(\mathcal{D})=g-d+r$. In particular we show the existence (and non-existence as well in some sporadic cases) of every Hilbert scheme of linearly normal curves with $i(\mathcal{D})=4$. We also determine the irreducibility of $\mathcal{H}^\mathcal{L}_{2r+4,r+8,r}$ for $3\le r\le 8$, which are rather peculiar families in a certain sense

Econometric Analysis of Erie County, NY Schools: The Effects of Poverty on Our Schools and Evaluating Possible Solutions

School districts in the Buffalo Metropolitan Area are very segregated by socioeconomic status which has resulted in very different educational outcomes for the region\u27s students as measured by New York State assessment results at the 4th grade and 8th grade level in English Language Arts and Math. This study measured the correlation between average test score results for each school building in Erie County and the rate of low-income students in those schools. The multiple regression analysis performed controlled for race, percentage of students that had a disability, class size, and per-pupil expenditures by the district. The study found that there was a strong negative correlation between test scores and the rate of low-income students in those schools. The average drop in score for a one percentage point increase in students that qualified for free and reduced price meals was about .3 points for 4th graders and about .2 points for 8th graders. The study also found that 100% of elementary schools in Erie County with fewer than 60% low-income students averaged a proficient score on the 2011 Math and ELA exams, while just 23% of schools with above 60% low-income students averaged a proficient score. This study concluded that to improve educational outcomes in areas where poverty is heavily concentrated in schools, an approach that involves socioeconomic integration of the Buffalo Metropolitan Area schools is needed. Other metro areas have successfully implemented such policies and should be used as a model to develop a plan going forward for the Buffalo region

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.Here we prove the projective normality of several special line bundles on a general k-gonal curve.* The author was partially supported by MIURST and GNSAGA of INdAM (Italy) ** The author was partially supported by KOSEF # R01-2002-000-00051-